A general analysis is presented for the scintillation index of a Gaussian beam wave propagating through a turbulent medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, the phase screen scintillation index agrees with that of a plane wave propagating through extended turbulence when the phase variance and spectrum for refractive index of the screen and extended medium are the same. However, for a finite Gaussian beam at the input plane, our analysis reveals that the distance from input plane to the phase screen must be many times greater than the distance from the screen to output plane to simulate a plane wave propagating through an extended medium.